中文摘要：

采用晶格动力学理论推导了计及次近邻原子作用下平面正三角晶格振动的色散关系,得到第一布里渊区中三种特殊对称方向的色散关系表达式;每一对称方向有两支声学波,其中Γ-M和Γ-K方向有一支纵波和一支横波,且纵波的频率高于横波的频率,而M-K方向两支声学波既非纵波、又非横波.探讨了次近邻原子作用对色散关系的影响,结果表明：在缺乏次近邻原子作用下,最近邻原子间作用足够在整个第一布里渊区产生振动频谱;随着次近邻原子间作用的增强,声子频率不断增大,Γ-M和M-K方向两声学支的频率间隙不断减小,Γ-K方向部分横波声子频率逐渐趋近于最近邻原子作用下的纵波声子频率,而其纵波声子频率的极大值显著增大.次近邻原子之间的相互作用对色散关系有显著的影响,但是声子频率在Γ和K点始终不变并分别简并.

英文摘要：

The dispersion relations were derived under the secondary neighbor coupling according to lattice dynamics,and the expressions of the dispersion relations along three symmetry directions were obtained in the first Brillouin zone.There are two pieces of acoustic branches in each direction,a longitudinal wave and a transverse wave are along Γ-M and Γ-K directions,and longitudinal wave frequencies are larger than transverse wave frequencies,but the two pieces of acoustic branches along M-K direction are neither longitudinal wave nor transverse wave.The effect of secondary neighbor coupling to the dispersion relations was studied.The results show that the vibration spectrum is sufficiently produced by the nearest neighbor coupling in the whole Brillouin zone with absence of secondary neighbor coupling;the phonon frequencies are continuously increased,and the frequency gap of two acoustic branches is gradually narrowed along Γ-M and M-K directions with the enhancement of the secondary neighbor coupling;a proportion of the transverse wave phonon frequencies are gradually closed to longitudinal wave phonon frequencies of the nearest neighbor coupling,and the maximum value of longitudinal wave phonon frequencies is distinctly increased along Γ-K direction.The above results indicate that the dispersion relations are remarkably affected by the secondary neighbor coupling.But the phonon frequencies remains unchanged at Γ and K points and they are degenerate.